JP2002162328A - Derivation method of material constitutive equation by indentation test - Google Patents
Derivation method of material constitutive equation by indentation testInfo
- Publication number
- JP2002162328A JP2002162328A JP2000360791A JP2000360791A JP2002162328A JP 2002162328 A JP2002162328 A JP 2002162328A JP 2000360791 A JP2000360791 A JP 2000360791A JP 2000360791 A JP2000360791 A JP 2000360791A JP 2002162328 A JP2002162328 A JP 2002162328A
- Authority
- JP
- Japan
- Prior art keywords
- indentation
- constitutive equation
- curve
- indenters
- load
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000007373 indentation Methods 0.000 title claims abstract description 36
- 239000000463 material Substances 0.000 title claims abstract description 34
- 238000000034 method Methods 0.000 title claims abstract description 17
- 238000012360 testing method Methods 0.000 title claims abstract description 9
- 238000009795 derivation Methods 0.000 title 1
- 238000002474 experimental method Methods 0.000 claims abstract description 7
- 238000005482 strain hardening Methods 0.000 claims description 8
- 238000005259 measurement Methods 0.000 claims 1
- 235000019589 hardness Nutrition 0.000 abstract description 20
- 238000010586 diagram Methods 0.000 description 5
- 238000006073 displacement reaction Methods 0.000 description 3
- 239000000956 alloy Substances 0.000 description 1
- 229910045601 alloy Inorganic materials 0.000 description 1
- 238000005260 corrosion Methods 0.000 description 1
- 230000007797 corrosion Effects 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 238000009501 film coating Methods 0.000 description 1
- 230000005855 radiation Effects 0.000 description 1
- 239000000523 sample Substances 0.000 description 1
- 239000002344 surface layer Substances 0.000 description 1
- 239000013077 target material Substances 0.000 description 1
- 239000010409 thin film Substances 0.000 description 1
Landscapes
- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
Abstract
(57)【要約】
【課題】 押込み荷重−押込み深さ曲線から材料の荷重
変形挙動を規定する構成式を導出する方法。
【解決手段】 Ｎ個の未知数を含む、決定しようとする
構成式を仮定した材料表面を対象とした、押し込み試験
に関する仮想数値実験を行う。そして、Ｎ個の形状の異
なる圧子から得られるＮ個の見かけの硬度とＮ個の未知
数の関係を表す特性曲線を有限要素法などにより数値解
析的に求める。次に、実験的にＮ個の圧子による押込み
荷重−押込み深さ曲線から見かけの硬度を求め、実測さ
れたＮ個の見かけの硬度と先に求めた特性曲線との関係
から、構成式中の定数を決定できる方法である。
(57) [Summary] [PROBLEMS] A method for deriving a constitutive equation defining a load deformation behavior of a material from an indentation load-indentation depth curve. A virtual numerical experiment related to an indentation test is performed on a material surface including N unknowns and on the assumption of a constitutive equation to be determined. Then, a characteristic curve representing a relationship between the N apparent hardnesses obtained from the N different indenters and the N unknowns is obtained by numerical analysis using a finite element method or the like. Next, the apparent hardness was experimentally determined from the indentation load-indentation depth curve by the N indenters, and from the relationship between the actually measured N apparent hardness and the previously determined characteristic curve, This is a method that can determine the constant.
Description
【０００１】[0001]
【発明の属する技術分野】本発明は、押込み荷重−押込
み深さ曲線から材料の荷重変形挙動を規定する構成式
（材料固有の、負荷荷重に対する変形挙動を規定する
式）を導出する方法に関するものである。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for deriving a constitutive equation for defining a load deformation behavior of a material (an equation for defining a material-specific deformation behavior with respect to a load) from an indentation load-indentation depth curve. It is.
【０００２】[0002]
【従来の技術】材料の荷重変形挙動を規定する構成式に
関して、ヤング率を除き、押込み試験から得られる情報
は、硬さあるいは半経験的な硬さと降伏応力との関係か
ら、降伏応力を定性的に評価する場合に限られていた。
このヤング率は押込み荷重除荷−押込み深さの関係から
求める方法が確立している。2. Description of the Related Art With respect to a constitutive equation for defining the load deformation behavior of a material, except for Young's modulus, information obtained from an indentation test is based on the relationship between hardness or semiempirical hardness and yield stress. It was limited to the case where it was evaluated on a regular basis.
A method has been established for obtaining this Young's modulus from the relationship between the indentation load unloading and the indentation depth.
【０００３】[0003]
【発明が解決しようとする課題】従来、押込み試験から
得られる定性的な情報を、定量的な情報として評価し、
工学設計に不可欠な材料の荷重変形挙動を記述できる構
成式を導出することが、本発明により解決しようとした
課題である。Conventionally, qualitative information obtained from an indentation test is evaluated as quantitative information,
It is an object of the present invention to derive a constitutive equation that can describe the load deformation behavior of a material indispensable for engineering design.
【０００４】[0004]
【課題を解決するための手段】得ようとする材料構成式
中に含まれる未知の定数の数に対応する複数の形状の異
なる圧子により、対象材料の押込み荷重−押込み深さ曲
線を得る。すなわち、圧子の数分（構成式中の未知な定
数の数分）の曲線を得る。各々の荷重と深さ曲線から見
かけの硬度を評価し、見かけの硬度に関する有限要素法
などによる数値解析から得られた特性曲線と実測された
見かけの硬度との関係から構成式中の各定数を決定する
ものである。An indentation load-indentation curve of a target material is obtained by a plurality of indenters having different shapes corresponding to the number of unknown constants included in the material constitutive expression to be obtained. That is, a curve for several indenters (the number of unknown constants in the constitutive equation) is obtained. Evaluate the apparent hardness from each load and depth curve, and calculate each constant in the constitutive equation from the relationship between the characteristic curve obtained from numerical analysis by the finite element method etc. on the apparent hardness and the actually measured apparent hardness. To decide.
【０００５】[0005]
【発明の実施の形態】Ｎ個の未知数を含む、決定しよう
とする構成式を仮定した材料表面を対象とした、押し込
み試験に関する仮想数値実験を行い、Ｎ個の形状の異な
る圧子から得られるＮ個の見かけの硬度とＮ個の未知数
の関係を表す特性曲線を周知の有限要素法などにより数
値解析的に求める。DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A virtual numerical experiment on an indentation test is performed on a material surface including N unknowns and on the assumption of a constitutive equation to be determined, and N values obtained from N indenters having different shapes are obtained. A characteristic curve representing a relationship between the apparent hardness and the N unknowns is obtained by numerical analysis using a well-known finite element method or the like.
【０００６】次に、実験的にＮ個の圧子による押込み荷
重−押込み深さ曲線から見かけの硬度を求め、実測され
たＮ個の見かけの硬度と先に求めた特性曲線との関係か
ら、構成式中の定数を決定できる方法である。Next, the apparent hardness is experimentally determined from the indentation load-indentation depth curve by the N indenters, and the configuration is determined from the relationship between the actually measured N apparent hardness and the previously determined characteristic curve. This is a method that can determine the constants in the equation.
【０００７】即ち、図２に示されるように、材料固有
の、負荷荷重に対する変形挙動を表わす複数（Ｎ個）の
未知の定数を含む材料構成式ｆｃを決定するために、Ｎ
個の圧子を用いた押込み荷重／深さー深さ曲線を得る。That is, as shown in FIG. 2, in order to determine a material constitutive equation fc including a plurality (N) of unknown constants representing a deformation behavior with respect to a load, which is inherent to the material,
The indentation load / depth-depth curve using the indenter is obtained.
【０００８】まず、材料表面の特性を評価するに当たっ
て、図２に示されるように、Ｎ個の形状の異なる圧子
（ｉ＝１、、ｉ、、Ｎ）それぞれについて、コンピュー
タを使用した仮想数値実験を行うことにより、その材料
の押込み荷重／深さー深さ曲線を数値解析的に得る。こ
の曲線の各々に基いて、図１の左図に示される等価硬度
（見かけ硬度）Ｓを、それぞれ、周知の有限要素法解析
（図３参照）を使用して得る。このＮ個の圧子に関して
得られた見かけ硬度Ｓｉに対する、図２に示されるよう
な材料構成式における材料に関する未知の定数であるＣ
ｉの関係について、図３に示されるような特性曲線を数
値解析的に得る。First, in evaluating the characteristics of a material surface, as shown in FIG. 2, virtual numerical experiments using a computer were performed on each of N indenters having different shapes (i = 1, i, N). Is performed, the indentation load / depth-depth curve of the material is obtained numerically. Based on each of these curves, the equivalent hardness (apparent hardness) S shown in the left diagram of FIG. 1 is obtained using a well-known finite element analysis (see FIG. 3). For the apparent hardness Si obtained for the N indenters, the unknown constant C for the material in the material constitutive equation as shown in FIG.
Regarding the relationship of i, a characteristic curve as shown in FIG. 3 is obtained by numerical analysis.
【０００９】次に、上記と同じ形状のＮ個の形状の異な
る圧子を用いて材料表面に対して押込み荷重実験を実際
に行って、その材料の押込み荷重／深さ−深さ曲線を
得、この曲線からそれぞれの圧子についての見かけ硬度
Ｓｉ、、Ｓ１、、ＳＮを得た。Next, an indentation load experiment was actually performed on the material surface using N different indenters having the same shape as described above, and an indentation load / depth-depth curve of the material was obtained. From this curve, apparent hardnesses Si, S1, and SN for each indenter were obtained.
【００１０】この実験的に得られた見かけ硬度Ｓ１、、
Ｓｉ、、ＳＮを、図３に示されるような方程式に挿入し
て、未知の定数であるＣｉを得る。そして、この得られ
たＮ個の数値を、図３の数値解析的に得られた、見かけ
硬度Ｓｉに対する未知の定数であるＣｉに関する特性曲
線から、得られた数値と比較して数値的に差異がないこ
とを検証する。The experimentally obtained apparent hardness S1,
Inserting Si, SN into the equation as shown in FIG. 3 to obtain unknown constant Ci. Then, the obtained N numerical values are numerically different from the obtained numerical values from the characteristic curve relating to Ci, which is an unknown constant with respect to the apparent hardness Si, obtained by numerical analysis in FIG. Verify that there is no
【００１１】なお、本発明で使用する形状の異なる圧子
は、図１に示されるような頂角の異なる３角錐圧子を使
用し、この圧子を試料材料の表面に押込むことにより、
図１に示される押込み荷重／深さー深さ曲線が得られ
る。As the indenter having a different shape used in the present invention, a triangular pyramid indenter having a different apex angle as shown in FIG. 1 is used, and the indenter is pressed into the surface of the sample material.
The indentation load / depth-depth curve shown in FIG. 1 is obtained.
【００１２】[0012]
【実施例】まず、ニッケル基合金の荷重変位挙動を表し
得る材料構成式として、図４に示す、指数関数型の構成
式を仮定する。指数関数型の構成式には、決定すべき未
知の定数は４つある。すなわち、ヤング率Ｅ（弾性係
数）、降伏応力（σｙ）、加工硬化指数ｎ、加工硬化係
数Ａである。ここで、ヤング率については、従来技術で
ある押込み荷重／深さ−深さ曲線より求めることができ
る。First, as a material constitutive equation capable of expressing the load displacement behavior of a nickel-base alloy, an exponential function type constitutive equation shown in FIG. 4 is assumed. In the exponential function type formula, there are four unknown constants to be determined. That is, Young's modulus E (elastic coefficient), yield stress (σy), work hardening index n, work hardening coefficient A. Here, the Young's modulus can be obtained from a conventional indentation load / depth-depth curve.
【００１３】したがって、図４に示すように、残りの３
つの未知数を決定しなければならない。そこで、本発明
に従って、３つの形状の異なる圧子を用意する。ここで
は、頂角の異なる三角錐圧子（等価円錐頂角：６３度、
７０度、７６度）を用いることとした。Therefore, as shown in FIG.
One unknown must be determined. Therefore, according to the present invention, indenters having three different shapes are prepared. Here, a triangular pyramid indenter with a different apex angle (equivalent cone apex angle: 63 degrees,
70 degrees, 76 degrees).
【００１４】まず、３つの圧子形状それぞれに従った仮
想数値実験を汎用有限要素法コードＤＹＮＡにより行
い、任意の定数を持つ指数関数型構成式を仮定した対象
材料（ニッケル基合金）の表面に対して、数値解析的に
押込み荷重／深さ−深さ曲線を得て、各三角錐圧子と見
かけの硬度の関係を任意の定数に対する特性曲線として
得た。First, a virtual numerical experiment according to each of the three indenter shapes is performed by a general-purpose finite element method code DYNA. Then, an indentation load / depth-depth curve was obtained by numerical analysis, and a relationship between each triangular pyramid indenter and apparent hardness was obtained as a characteristic curve for an arbitrary constant.
【００１５】次に、実験により３つの圧子による押込み
荷重／深さ−深さ曲線から見かけの硬度を実測した。実
測された見かけの硬度と特性曲線から、図４の指数関数
型構成式の定数である降伏応力σｙ、加工硬化指数ｎ、
加工硬化係数Ａを決定した。Next, an apparent hardness was actually measured from an indentation load / depth-depth curve by three indenters by an experiment. From the measured apparent hardness and the characteristic curve, the yield stress σy, the work hardening index n,
The work hardening coefficient A was determined.
【００１６】決定した構成式を導入して解析的に評価し
た単軸引張荷重変位曲線は、実験的に評価された荷重変
位曲線を良く表すことから、本発明の有用性を確認でき
た。The usefulness of the present invention could be confirmed because the uniaxial tensile load-displacement curve analytically evaluated by introducing the determined constitutive equation well represented the experimentally evaluated load-displacement curve.
【００１７】[0017]
【発明の効果】特に、押込み領域が小さい場合、微小試
験技術への応用として本方法は有効である。具体的に
は、放射線照射材料、薄膜被覆材、腐食表層部等の材料
特性評価方法としての応用が期待できる。In particular, when the indentation area is small, the present method is effective as an application to a micro test technique. Specifically, it can be expected to be applied as a material property evaluation method for radiation irradiation materials, thin film coating materials, corrosion surface layers, and the like.
【図１】 形状の異なる圧子、それを用いた押込み荷重
／深さー深さ曲線を示す図である。FIG. 1 is a diagram showing indenters having different shapes and indentation load / depth-depth curves using the indenters.
【図２】 複数の未知の定数を含む材料構成式と複数の
圧子から得た押込み荷重／深さー深さ曲線を示す図であ
る。FIG. 2 is a diagram showing a material constitutive equation including a plurality of unknown constants and an indentation load / depth-depth curve obtained from a plurality of indenters.
【図３】 材料構成式を導出するための方法を示す図で
ある。FIG. 3 is a diagram showing a method for deriving a material constitutive equation.
【図４】 材料構成式の導出例を示す図である。FIG. 4 is a diagram showing an example of deriving a material constitutive equation.
───────────────────────────────────────────────────── フロントページの続き (72)発明者 井岡 郁夫 茨城県那珂郡東海村白方字白根２番地の４ 日本原子力研究所東海研究所内 (72)発明者 田辺 裕治 新潟県新潟市五十嵐二の町8050番地 新潟 大学内 ──────────────────────────────────────────────────続 き Continuing from the front page (72) Inventor Ikuo Ioka 2-4, Shirane, Shirakata, Tokai-mura, Naka-gun, Ibaraki Pref. Niigata University
Claims (3)
試験から材料表面の特性を評価するための材料構成式を
導出する方法。1. A method for deriving a material constitutive equation for evaluating a material surface property from an indentation test using a plurality of indenters having different shapes.
込み荷重−押込み深さ曲線と数値解析から得られる特性
曲線を融合して材料構成式を導出する方法。2. A method for deriving a material constitutive equation by fusing an indentation load-indentation depth curve obtained from a plurality of indenters having different shapes and a characteristic curve obtained from numerical analysis.
において、 ａ） 材料構成式中の未知の定数の数に対応する複数の
形状の異なる圧子について、コンピュータによる仮想数
値実験を行って材料の押込み荷重ー押込み深さ曲線を数
値解析的に得、 ｂ） この曲線の各々に基いて見かけの硬度（等価硬
度）を周知の有限要素法解析（ＦＥＭ）によりそれぞれ
得、 ｃ） この得られた見かけ硬度と材料構成式における未
知の定数である降伏応力、加工硬化係数及び加工硬化指
数等との関係についての特性曲線を得、 ｃ） 同じ３種類の形状の異なる圧子を用いて材料表面
に対して押込み実験を実際に行って、その材料の押込み
荷重ー押込み深さ曲線を得、この曲線からそれぞれの圧
子についての見かけ硬度を得、 ｄ） この実験的に得られた見かけ硬度を、材料構成式
に挿入して、未知の定数である降伏応力、加工硬化係数
及び加工硬化指数等を得、 ｅ） この実測により得られた数値を、上記数値解析的
に得られた特性曲線から得られた数値と比較して数値的
に近似していることを検証することからなる、 上記方法。3. A method of deriving a material constitutive equation by an indentation test, comprising the steps of: a) performing a virtual numerical experiment with a computer on a plurality of indenters having different shapes corresponding to the number of unknown constants in the material constitutive equation to indent the material; A load-indentation depth curve is obtained numerically; b) an apparent hardness (equivalent hardness) is obtained by a well-known finite element method analysis (FEM) based on each of the curves; c) the obtained apparent value A characteristic curve is obtained for the relationship between the hardness and the yield stress, work hardening coefficient, work hardening index, etc., which are unknown constants in the material constitutive equation. C) The same three types of different indenters having different shapes are used for the material surface. The indentation test was actually performed to obtain an indentation load-indentation depth curve of the material, and from this curve, the apparent hardness of each indenter was obtained. The hardness is inserted into the material constitutive equation to obtain unknown constants, such as yield stress, work hardening coefficient and work hardening index. E) The numerical value obtained by the actual measurement is converted into the characteristic obtained by the above numerical analysis. Verifying numerical approximation by comparing with a numerical value obtained from a curve.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2010101876A (en) * | 2008-09-29 | 2010-05-06 | Ihi Corp | Material property specification method of elastoplastic material by indentor indentation test |
| KR101615934B1 (en) * | 2014-08-07 | 2016-05-09 | 울산과학기술원 | Selection method of costitutive equations |
| CN113776912A (en) * | 2021-09-16 | 2021-12-10 | 齐鲁工业大学 | Method for rapidly determining chemical stability of medicinal glass |
-
2000
- 2000-11-28 JP JP2000360791A patent/JP2002162328A/en active Pending
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2010101876A (en) * | 2008-09-29 | 2010-05-06 | Ihi Corp | Material property specification method of elastoplastic material by indentor indentation test |
| KR101615934B1 (en) * | 2014-08-07 | 2016-05-09 | 울산과학기술원 | Selection method of costitutive equations |
| CN113776912A (en) * | 2021-09-16 | 2021-12-10 | 齐鲁工业大学 | Method for rapidly determining chemical stability of medicinal glass |
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